Multi-scale Modeling of Nano-Particle Reinforced Polymers in the Nonlinear Regime

Roy, Samit; Akepati, Avinash Reddy; Hayes, Nicholas

doi:10.2514/6.2012-1822

Cited by 3 publications

(5 citation statements)

References 19 publications

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“…The discrete atomistic values of potentials and displacement gradients obtained from MD simulations were converted into field quantities using the finite element interpolation functions for a nine node element (i.e., set K=9 in Eq. (3) and (4)) 31 .…”

Section: Atomistic J-integral Evaluation Methodologymentioning

confidence: 98%

“…(5),  f is the vector representing the force between atoms  and  ,  X is the vector representing the difference in their positions, and B  is the bond function defined by Hardy 26 . A detailed description for evaluation of each term required to calculate atomistic J-integral can be found elsewhere 31 . From statistical mechanics, the Helmholtz free energy density is given by 29 ,…”

Section: Atomistic J-integral Evaluation Methodologymentioning

confidence: 99%

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Modeling of Fracture in Nano-Particle Reinforced Polymers using the Atomistic J-Integral

Akepati

Roy

Unnikrishnan

2015

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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In order to better understand the local influence of nano-particle on the mechanical properties of the polymer, nano-scale analysis is necessary. In that context, this paper is directed towards understanding damage initiation and failure progression in advanced nanostructured composite materials using molecular dynamics. The critical value of the Jintegral (JIC) at crack initiation is related to the fracture toughness of the material, where the subscript I denotes the fracture mode (I=1, 2, 3). Therefore, the J-integral could be used as a suitable metric for estimating the crack driving force as well as the fracture toughness of the material as the crack begins to initiate. Further, the conventional isothermal definition of Jintegral does not take into account the entropic contribution to the free energy, and consequently, may lead to significant over-estimation of the J-integral at the atomistic level, especially at finite temperatures. As a case study, the feasibility of computing the dynamic atomistic J-integral over the molecular dynamics (MD) domain at finite temperature is evaluated for a graphene nano-platelet and the values are compared with results from linear elastic fracture mechanics (LEFM) for isothermal crack initiation at 0 K and at 300 K. Jintegral computations are also done using ReaxFF force field in order to simulate bond breakage during crack propagation. Good agreement is observed between the atomistic J and the LEFM results at 0 K, with predictable discrepancies at 300 K due to entropic effects. A novel cohesive-contour based methodology for computing J-integral is discussed and successfully applied to a graphene nano-platelet. Work is currently underway to compute Jintegral for nanographene modified EPON 862 at 0.1 K and 300 K using the cohesive-contour based procedure and to be able to computationally predict fracture toughness. In order to account for the high strain-rates encountered in MD simulations, scaling laws will be developed to correlate fracture toughness predicted by the MD simulations to the toughness data obtained from compact tension fracture experiments. NomenclatureK = Kelvin B k = Boltzmann constant LAMMPS = Large-scale Atomic/Molecular Massively Parallel Simulator MD = Molecular Dynamics nm = Nanometer P = 1 st Piola-Kirchhoff stress tensor Ψ = Free energy density ψ = Localization function S = Eshelby stress tensor 1 Professor,

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Section: Atomistic J-integral Evaluation Methodologymentioning

confidence: 98%

Section: Atomistic J-integral Evaluation Methodologymentioning

confidence: 99%

Modeling of Fracture in Nano-Particle Reinforced Polymers using the Atomistic J-Integral

Akepati

Roy

Unnikrishnan

2015

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…(2) are given below. A detailed description for evaluation of each term required to calculate atomistic J-integral is given in Roy et al 17 . American Institute of Aeronautics and Astronautics In Eq.…”

Section: Atomistic J-integral Evaluation Methodologymentioning

confidence: 99%

“…As discussed in Ref. (17), the discrete atomistic values of potentials and displacement gradients are converted into field quantities using the finite element interpolation functions for a nine node element (i.e., K=9 in Eq. (3) and (4)).…”

Section: Numerical Evaluation Of Atomistic J-integralmentioning

confidence: 99%

Multi-scale Modeling of Failure in Nano-Particle Reinforced Polymers Using the Atomistic J-Integral

Roy

Akepati

2014

55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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This paper is directed towards understanding damage initiation and failure progression in advanced nanostructured composite materials using hierarchical coupling of molecular dynamics with micromechcanics and continuum mechanics. The molecular dynamics method is a subset of computational chemistry codes which creates system trajectories consistent with thermo-dynamic ensembles. The molecular dynamics program LAMMPS, (Large-scale Atomic/Molecular Massively Parallel Simulator) is a versatile code with numerous functionalities which can be used to simulate polymer systems. Although, the results for molecular simulation models, in particular polymer models are system size dependent, the ease with which large molecular systems can be evaluated, especially with parallel molecular dynamics codes such as LAMMPS makes it a more attractive choice compared to other approaches such as ab-initio calculations, which are limited to the calculation of a few 100 atoms. The critical value of the J-integral (J I ) at crack initiation is related to the fracture toughness of the material, where the subscript I denotes the fracture mode (I=1, 2, 3). Therefore, the J-integral could be used as a suitable metric for estimating the crack driving force as well as the fracture toughness of the material as the crack begins to initiate. However, for the conventional macroscale definition of the J-integral to be valid at the nanoscale in terms of the continuum stress and displacement fields and their spatial derivatives requires the construction of local continuum fields from discrete atomistic data, and using these data in the conventional contour integral expression for atomistic J-integral. One such methodology is proposed by Hardy that allows for the local averaging necessary to obtain the definition of free energy, deformation gradient, and Piola-Kirchoff stress as fields (and divergence of fields) and not just as total system averages. Further, the conventional isothermal definition of J-integral does not take into account the entropic contribution to the free energy, and consequently, may lead to significant over-estimation of the J-integral at the atomistic level, especially at finite temperatures. As a case study, the feasibility of computing the dynamic atomistic J-integral over the MD domain at finite temperature using Hardy estimates of continuum fields based on localization functions is evaluated for a graphene nano-platelet. For model verification, the values of atomistic J-integral are compared with results from linear elastic fracture mechanics (LEFM) for isothermal crack initiation at 0 K and at 300 K. Good agreement is observed between the atomistic J and the LEFM results at 0 K, with predictable discrepancies at 300 K due to entropic effects. Finally, a nano-micro-macro hierarchical multi-scale model is presented that is capable of simulating progressive damage evolution in a composite aerospace structural component. NomenclatureK = Kelvin B k = Boltzmann constant LAMMPS = Large-scale Atomic/Molecular Massively Parallel Simu...

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“…However, bond dissociation occurring past the yield stress was not considered in both these studies, and the effects of bond rotation and van der Waals interactions alone were addressed. Roy and co-workers investigated the nonlinear behavior of polymers through molecular simulations using the atomistic J-integral based on Hardy estimates of continuum stresses [11]. While a few approaches involving the use of the finitely extensible nonlinear elastic (FENE) force field [12] have captured fracture successfully, the strains at which failure is observed do not correlate with experimental results.…”

Section: Introductionmentioning

confidence: 99%

Molecular dynamics-based multiscale damage initiation model for CNT/epoxy nanopolymers

et al. 2017

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A methodology that accurately simulates the brittle behavior of epoxy polymers initiating at the molecular level due to bond elongation and subsequent bond dissociation is presented in this paper. The system investigated in this study comprises a combination of crystalline carbon nanotubes (CNTs) dispersed in epoxy polymer molecules. Molecular dynamics (MD) simulations are performed with an appropriate bond order-based force field to capture deformation-induced bond dissociation between atoms within the simulation volume. During deformation, the thermal vibration of molecules causes the elongated bonds to reequilibrate; thus, the effect of mechanical deformation on bond elongation and scission cannot be captured effectively. This issue is overcome by deforming the simulation volume at zero temperature-a technique adopted from the concept of quasi-continuum and demonstrated successfully in the authors' previous work. Results showed that a combination of MD deformation tests with ultra-high strain rates at near-zero temperatures provides a computationally efficient alternative for the study of bond dissociation phenomenon in amorphous epoxy polymer. In this paper, the ultra-high strain rate deformation approach is extended to the CNT-epoxy system at various CNT weight fractions and the corresponding bond disassociation energy extracted from the simulation volume is used as input to a low-fidelity continuum damage mechanics (CDM) model to demonstrate the bridging of length scales and to study matrix failure at the microscale. The material parameters for the classical CDM model are directly obtained from physics-based atomistic simulations, thus improving the accuracy of the multiscale approach.

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Multi-scale Modeling of Nano-Particle Reinforced Polymers in the Nonlinear Regime

Cited by 3 publications

References 19 publications

Modeling of Fracture in Nano-Particle Reinforced Polymers using the Atomistic J-Integral

Modeling of Fracture in Nano-Particle Reinforced Polymers using the Atomistic J-Integral

Multi-scale Modeling of Failure in Nano-Particle Reinforced Polymers Using the Atomistic J-Integral

Molecular dynamics-based multiscale damage initiation model for CNT/epoxy nanopolymers

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